AP Statistics · Summary

Unit 2 summary

1. For a conditional proportion, the group named after "of" or "given" is the group whose total goes in the denominator.
2. $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$ and $P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}$. Show independence by comparing $P(A \mid B)$ with $P(A)$ in numbers.
3. The mean of a random variable is $\sum x_i p_i$, read as a long-run average. For independent variables, means add or subtract and variances always add.
4. Use the binomial model only for a fixed number of independent success-or-failure trials with the same p; its mean is np and its standard deviation is $\sqrt{np(1-p)}$.
5. For normal models, convert to z, find the area, and for a percentile go from the area back to z and then to x.
6. A sample proportion has mean p and standard deviation $\sqrt{\frac{p(1-p)}{n}}$, and it is about normal when $np$ and $n(1-p)$ are both at least 10.
7. A sample mean has mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$, and for large n it is about normal even when the population is skewed.